When Shelf Life Matters: Multi-period Shelf-space Optimization

Grocery retailers must continually refine their product offerings to maintain customer attractiveness while safeguarding profitability and reducing food waste, a challenge that is particularly pronounced for perishables. Heterogeneous shelf lives, spoilage risk, customers' expiry-date preferences, and stochastic, period-specific demand create substantial operational complexity because these factors evolve over time and interact across periods. Addressing these characteristics requires a multi-period model that integrates assortment, shelf-space, and inventory decisions. Prevailing approaches, largely based on single-period models, overlook the fact that perishables are sold, replenished, and withdrawn over multiple periods. As a result, inventories contain units with different remaining shelf lives, which directly influence customers' expiry-date-dependent purchasing behavior and subsequent inventory dynamics.&nbsp; <div> We develop a novel integrated multi-period model to optimize assortment, shelf space, and inventory for packaged perishables. The model accounts for heterogeneous inventories, product expiration over time, weekly demand patterns, replenishment operations, and customers' expiry-date-dependent withdrawals. To address the resulting NP-hard knapsack problem with stochastic, nonlinear demand and dynamic inventory transitions, we propose a tailored simulationoptimization approach that iteratively updates demands. Using real-world data, we show that explicitly incorporating shelf lives, weekly demand patterns, and customer withdrawal behavior materially changes optimal assortment, shelf-space, and inventory decisions. We generalize the findings with simulated data and demonstrate the substantial potential to increase profitability while simultaneously reducing food waste. </div>